Wait a second!
More handpicked essays just for you.
More handpicked essays just for you.
Children's mathematical mind
Don’t take our word for it - see why 10 million students trust us with their essay needs.
Recommended: Children's mathematical mind
Content Analysis of Student Learning
For most people who have ridden the roller coaster of primary education, subtracting twenty-three from seventy is a piece of cake. In fact, we probably work it out so quickly in our heads that we don’t consciously recognize the procedures that we are using to solve the problem. For us, subtraction seems like something that has been ingrained in our thinking since the first day of elementary school. Not surprisingly, numbers and subtraction and “carry over” were new to us at some point, just like everything else that we know today. For Gretchen, a first-grader trying to solve 70-23, subtraction doesn’t seem like a piece of cake as she verbalizes her confusion, getting different answers using different methods. After watching Gretchen pry for a final solution and coming up uncertain, we can gain a much deeper understanding for how the concept of subtraction first develops and the discrepancies that can arise as a child searches for what is correct way and what is not.
After Gretchen is given the problem, she approaches it with her first method: the standard algorithm. To start off, she sets up the problem by writing out “70” and writing “- 23” directly below it, finishing out with a line underneath. This setup indicates several things about Gretchen’s basic mathematical understanding. First, it shows that she understands a connection between the words and the actual written symbols for each number. Also, since she writes “70,” Gretchen probably has knowledge of numbers up to ninety-nine. Last, her arrangement of the numbers indicates that she has knowledge of the minus being a symbol for “take away” and the second number be placed underneath the first. As she works the problem and su...
... middle of paper ...
... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.
References
IMAP, Gretchen, 2nd grade interview
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
References
IMAP, Gretchen, 2nd grade interview
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
Math is the study of patterns, with students learning to create, construct, and describe these patterns ranging from the most simple of forms to the very complex. Number sense grows from this patterning skill in the very young student as he/she explores ordering, counting, and sequencing of concrete and pictorial items. The skill of subitizing, the ability to recognize and discriminate small numbers of objects (Klein and Starkey 1988), is basic to the students’ development of number sense. In the article “Subitizing: What is it?
middle of paper ... ... Barr, C., Doyle, M., Clifford, J., De Leo, T., Dubeau, C. (2003). "There is More to Math: A Framework for Learning and Math Instruction” Waterloo Catholic District School Board Burris, A.C. "How Children Learn Mathematics." Education.com.
Children can enhance their understanding of difficult addition and subtraction problems, when they learn to recognize how the combination of two or more numbers demonstrate a total (Fuson, Clements, & Beckmann, 2011). As students advance from Kindergarten through second grade they learn various strategies to solve addition and subtraction problems. The methods can be summarize into three distinctive categories called count all, count on, and recompose (Fuson, Clements, & Beckmann, 2011). The strategies vary faintly in simplicity and application. I will demonstrate how students can apply the count all, count on, and recompose strategies to solve addition and subtraction problems involving many levels of difficulty.
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
Wu, Y. (2008). Experimental Study on Effect of Different Mathematical Teaching Methodologies on Students’ Performance. Journal of Mathematics Studies. Vol 1(1) 164-171.
The more common notion of numeracy, or mathematics in daily living, I believe, is based on what we can relate to, e.g. the number of toasts for five children; or calculating discounts, sum of purchase or change in grocery shopping. With this perspective, many develop a fragmented notion that numeracy only involves basic mathematics; hence, mathematics is not wholly inclusive. However, I would like to argue here that such notion is incomplete, and should be amended, and that numeracy is inclusive of mathematics, which sits well with the mathematical knowledge requirement of Goos’
Ward (2005) explores writing and reading as the major literary mediums for learning mathematics, in order for students to be well equipped for things they may see in the real world. The most recent trends in education have teachers and curriculum writers stressed about finding new ways to tie in current events and real-world situations to the subjects being taught in the classroom. Wohlhuter & Quintero (2003) discuss how simply “listening” to mathematics in the classroom has no effect on success in student academics. It’s important to implement mathematical literacy at a very young age. A case study in the article by authors Wohlhuter & Quintero explores a program where mathematics and literacy were implemented together for children all the way through eight years of age. Preservice teachers entered a one week program where lessons were taught to them as if they were teaching the age group it was directed towards. When asked for a definition of mathematics, preservice teachers gave answers such as: something related to numbers, calculations, and estimations. However, no one emphasized how math is in fact extremely dependable on problem-solving, explanations, and logic. All these things have literacy already incorporated into them. According to Wohlhuter and Quintero (2003), the major takeaways from this program, when tested, were that “sorting blocks, dividing a candy bar equally, drawing pictures, or reading cereal boxes, young children are experienced mathematicians, readers, and writers when they enter kindergarten.” These skills are in fact what they need to succeed in the real-world. These strategies have shown to lead to higher success rates for students even after they graduate
Breaking down tasks into smaller, easier steps can be an effective way to teach a classroom of students with a variety of skills and needs. In breaking down the learning process, it allows students to learn at equal pace. This technique can also act as a helpful method for the teacher to analyze and understand the varying needs of the students in the classroom. When teaching or introducing a new math lesson, a teacher might first use the most basic aspects of the lesson to begin the teaching process (i.e. teach stu...
Students will identify the correct how to find the area of circles. We are going to do this first by deriving the formula for the area of a circle ourselves. Students use these operations to solve problems. Students extend their previous understandings of finding the area of a shape: This learning goal meets the Common Core Standard CCSS.MATH.CONTENT.6.G.A.3. The students are going to learn find the area of only the doughnut, excluding the hole in the middle. For the formative assessments during the teaching of this unit, I will keep an observation log, where I note any student progress, whether it be positive or negative. I believe it will be important to record observations any time a student has difficulty with a particular task. For example, if a student has trouble solving the problems with the formulas. to purchase an item, I should write down particular actions, attitudes, and behaviors that stand out, as well as the specific issue. Any time the students are doing independent work, I will monitor the learning activities and record observations.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
Kirova, A., & Bhargava, A. (2002). Learning to guide preschool children's mathematical understanding: A teacher's professional growth. 4 (1), Retrieved from http://ecrp.uiuc.edu/v4n1/kirova.html
Silver, E. A. (1998). Improving Mathematics in Middle School: Lessons from TIMSS and Related Research, US Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328.
...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ.
Allowing children to learn mathematics through all facets of development – physical, intellectual, emotional and social - will maximize their exposure to mathematical concepts and problem solving. Additionally, mathematics needs to be integrated into the entire curriculum in a coherent manner that takes into account the relationships and sequences of major mathematical ideas. The curriculum should be developmentally appropriate to the